Method

We use the PAH kinetic model of Andrews et al. (2016). This model only considered hydrogenation of PAHs. Therefore, modifications had to be made to include the deutera- tion of PAHs.

We consider 3 PAHs of increasing size within thecoronene family: coronene C24H12, circumcoronene C54H18, and circumcircumcoronene C96H24. These species span the range of astrophysically relevant PAH sizes (Allamandola et al. 1989), and they are expected to be among the most stable PAHs in the ISM (Ricca et al. 2012). Coronene has a carbon core with 12 H atoms attached in pairs to 6 different rings (i.e., 6 duo rings). Circumcoronene has 12 H atoms attached in pairs to 6 separate rings (6 duo rings), and 6 H atoms attached to other 6 peripheral rings (6 solo rings). Circumcircumcoronene has similarly 6 duo rings and 12 solo rings.

Each PAH is characterized by the total number of edge atoms Nedge=NH+ND, where NHis the total number of H atoms attached at their periphery, and NDthe total number of D atoms attached at their periphery. We refer to homogenic PAHs as those having either only H atoms (ND =0) or only D atoms (NH=0). Heterogenic PAHs are those having both H and D atoms in a given ratio (also referred as PAHDs). Those PAHs with all outer edge C atoms occupied are referred to as the normal molecules, i.e., molecules having the

Figure 4.1: Position of a deuterium atom in circumcoronene derivatives. Here we consider molecules with only 1 D atom as an example of heterogenic species. Carbon cores are depicted in grey, H atoms are depicted in white, and D atoms are depicted in orange. From left to right we see C54H17D, and two isomers of C54H18D. The C54H17D molecule has the D atom in an aromatic position. The

heterogenic molecules with Nedge =19 on the other hand, can have an HH aliphatic group while keeping the D atom in an aromatic position; or can have an HD aliphatic group, while having only H atoms in aromatic positions.

total number of edge atoms Nedge=N0_H, where N0_H=12, 18 and 24 for coronene, circum- coronene and circumcircumcoronene, respectively. Species with 0<Nedge<N0_Hare called partial species, while those having Nedge>N0_Hare in super states.

For the sake of simplicity, we consider that these PAHs can vary their edge occupation (i.e., total number of edge atoms) from being completely devoid of edge atoms (NH=0 and ND=0) to having up to 2 extra edge atoms (i.e., Nedge=N0_H+2). We limit ourselves to super states of only+2 as this reduces the number of isomers. Given that the larger molecules are not usually found in highly de-hydrogen/deuterated partial states, we also consider that D atoms can only be attached to the duo rings of the PAHs, that is, all solo rings have only H atoms in them. Thus, the smallest deuterated species for coronene, circumcoronene and circumcircumcoronene are C24D, C54H6D and C96H12D, respectively. Both these choices are also supported by the IR studies and neither of these choices has an important impact on our results, but they considerably speed up the computing time.

For the upcoming analysis it is important to keep in mind then that for partial species with Nedge>Nsolo, deuterium atoms are attached to an aromatic position (see Figure 4.1);

while for species in super states deuterium can be attached to either an aromatic position or an aliphatic position (Figure 4.1). Regarding ionization states, we considered anions (Z =-1), neutrals (Z =0) and cations (Z =1). Other states are not relevant under the physical conditions we probe.

4.2.2. Molecular Properties

We use the molecular characteristics described in Andrews et al. (2016). Given the lack of specific molecular properties for deuterated species, we decided to use the prop- erties of the homogenic hydrogenated species in Andrews et al. (2016) for all (deuterated and heterogenic) isomers with the same number of edge atoms. This includes the ion-

Figure 4.2: Comparison of the IR emission and photodissociation rates for H and D losses as a function of internal energy of the PAHs. The rates determined for coronene, circumcoronene and circumcir- cumcoronene derivatives are shown in black, blue and red, respectively. The left panel shows the rates for the PAHs in partial states with a total number of edge atoms Nedge=N0H−1, where N

0 His the

number of edge atoms of the PAHs in their normal state (i.e., 12 for coronene, 18 for circumcoronene and 24 for circumcircumcoronene). We have plotted these to exemplify the rates for molecules with an odd number of edge atoms. The middle panel shows the rates for the normal state molecules, exemplifying also the rates for PAHs with an even number of edge atoms. The right panel shows the rates for the first super-state molecules (i.e., with Nedge=N0H+1) to illustrate the rates for super-state

PAHs.

ization potentials (IP) and electron affinities (EA) (i.e., the inverse linear relation between these energies and the edge occupation of each PAH), ionization yields, UV absorption cross sections, polarizabilities, IR cross sections and density of states.

4.2.3. Reactions with Deuterium

As mentioned before, Andrews et al. (2016) included ionization and electron recom- bination of PAHs, (multiphoton) H and H2 dissociation processes, reactivity with H, and Eley-Rideal abstraction of H2from superhydrogenated species. Here, we include PAH re- activity with D, direct D-loss through photodissociation, and Eley-Rideal abstraction of D2 and HD from species in super states. It is important to mention that we will not consider H2photodissociation, since this process will hardly compete against H and D losses in the environments sampled in this work (Andrews et al. 2016).

Photodissociation

Photodissociation rates of H-loss are calculated using the same activation energies and entropies as in Andrews et al. (2016). For species in partial states we then consider acti- vation energies ofEact =4.6 and 4.1 eV, and entropies of∆S =44.8 and 55.6 J/K/mol, for

species having an even and odd number of edge atoms, respectively (and for all charge states admitted in the model). In order to calculate the photodissociation rate of D-loss from species in partial states, we modified the energies taking into account the different zero-point energies of C-H and C-D bonds (i.e., 0.09 eV). This value comes from a compar- ison between the ZPE of CH4 and CD4 molecules using calculations at the B3LYP/4-31G level. No scaling was applied to the ZPE to account for anharmonicity.

Figure 4.2 shows a comparison of the IR emission and the photodissociation rates as a function of internal energy of hydrogenated PAHs. This illustrates that there are only minor differences in the resulting H and D-loss rates over the relevant energy range.

We consider that the partial species first lose all the edge atoms in duo rings. For PAHs with an even number of edge atoms we include a term in the estimation of the j-loss rate, to account for the number of H and D atoms in each molecule:

ekj=

Nj,duo

(Nedge−Nsolo)

kj (4.1)

wherekjis the loss rate given by expression (7) in Andrews et al. (2016); andNj,duocorre-

sponds to the total number of jatoms in duo rings that the PAH can lose. For PAHs with an odd number of edge atoms we considerekj=kjsince the PAH will lose the edge atom

left alone in the duo ring. Once all edge atoms in duos are stripped off the PAH, then the molecule starts losing the solo H-atoms withEact=4.6 eV, and change in entropy of∆S =

44.8 J/K/mol (see more in Andrews et al. 2016).

Regarding PAHs in super states, for the H-loss we adopt the binding energies of an extra H-atom in a duo position, which are of 1.4 eV for the anion, 1.4 eV for the neutral and 1.55 eV for the cation, and an activation entropy of 55.6 J/K/mol (Bauschlicher & Ricca 2014). For the D-loss we again consider the 0.09 eV difference in the activation energy with respect to the values used for the H-loss (Figure 4.2). We assume extra H and D atoms always stick to duo positions for all molecules. For PAHs with an even number of edge atoms we also include a term in the estimation of the photodissociation rate of j-loss, to account for the number of H and D atoms in aliphatic groups:

ekj=

Nj,alip

(NH,alip+ND,alip)

kj (4.2)

where in this case, NH,alipand ND,alipcorrespond to the total number of H and D atoms in aliphatic groups, respectively. For PAHs with an odd number of edge atoms we consider

ekH =kH in case the PAH has a H2 left;ekD=kDin case the PAH has a D2 left; andekH =

0.5×kHandekD=0.5×kDin case the PAH has an HD left.

Figure 4.3 shows the variation of the D-loss rates withG0for the heterogenic species with ND=1 and Nedge=N0_H−1, N0_H, and N0_H+1. Regarding partial and normal species, we see that for coronene single-photon events dominate, while for the larger PAHs multiphoton events take place. For PAHs in super states on the other hand, due to the low activation energies, single-photon events dominate for all species. These results are very much in line with those obtained for the corresponding H-loss rates, since the energy differences between C-D and C-H bonds are small.

Addition Rates

For positively ionized species we consider the H addition rate derived from the experi- ments of Le Page et al. (1997) on the hydrogenation of coronene, that is a rate of 1.4×10−10 cm3/s (see Andrews et al. 2016). We use this rate for all positively ionized species and for all Nedgestates. For D addition we divide this rate by a factor of

√

mD/mH∼1.4 to take into account the slightly larger mass of the D atom,mD, over that of the H atom,mH.

Figure 4.3: Deuterium loss rates through photodissociation as a function of the intensity of the UV field,G0. These rates are the resulting one considering also the H-loss and IR emission as relaxation channels. The rates are shown for neutral heterogenic molecules with 1 D atom in their edges. The black curves refer to coronene molecules, while the blue and red curves refer to circumcoronene and circumcircumcoronene molecules respectively. The left panel shows the D-loss rates for the partial-state PAHs C24H10D, C54H16D and C96H22D, with the D atom alone in a duo ring. As in Figure 4.2 we have plotted these to exemplify the rates for molecules with an odd number of edge atoms. The middle panel shows the rates for the heterogenic normal molecules (i.e., Negde=N0H): C24H11D,

C54H17D and C96H23D. The right panel shows the rates for the heterogenic molecules in the first super-state with an HD aliphatic group: C24H12D, C54H18D and C96H24D. For coronene molecules

the rates scale linearly withG0, while for the larger species multiphoton events are important for the normal and partial derivatives. The D-loss rate for the super-state molecules on the other hand, changes linearly withG0for all species.

For neutral PAHs we use the geometrical cross sections of each molecule,σgeom, to- gether with the energy barriers given by Rauls & Hornekær (2008) for the H addition to neutral coronene:

kj,add=σgeom

s

8kBTgas

πmj

exp(−Ebarrier/kB/Tgas), (4.3)

wherekBis the Boltzmann constant;Tgasis the gas temperature;Ebarrieris the energy barrier

for the addition; andmjis the mass of the jatom reacting with the PAH. For super states

we consider the energy barriers from Rauls & Hornekær (2008) for both H and D addition. For the partial species we do not consider any barriers (Ebarrier=0), and we adopt a 7%

efficiency as found for cations by Demarais et al. (2014). The H and D addition reactions to anionic PAHs on the other hand, is considered as a dissociative attachment process (De- marais et al. 2012). That is, the H addition rate is 7.8×10−10cm3/s. Again for the D addition rate we divide by a factor of∼1.4 to account for the different atomic masses, which leads to a D addition rate of 5.5×10−10 cm3/s for anionic molecules.

It is important to keep in mind that for PAHs in super states, we must consider the edge atoms each PAH has prior to the atom addition, since this determines whether there will be an H2, HD or D2 new aliphatic group in the PAH. To include this, we consider an extra factor in the reaction rate given by Pj =Nj,duo/(NH,duo+ND,duo), where NH,duo

Table 4.1: Physical conditions used in the model.

Model G0(Habing units) n(cm−3) nD(cm−3)

Diffuse Cloud 1 500 0.016

PDR 1000 106 ₁₆

and ND,duo correspond to the number of aromatic H and D atoms in duos prior to any

additions, respectively. Thus, for example, the PAH CaHbDcwith an HD aliphatic group

will form from the H addition to the corresponding isomer(s) of the PAH CaHb−1Dc, where the reaction rate is given byPD(CaHb−1Dc)×kH,add(CaHb−1Dc); and it will form from the D addition to the corresponding isomer(s) of the PAH CaHbDc−1, where the rate is given by

PH(CaHbDc−1)×kD,add(CaHbDc−1).

Abstraction Rates

We consider the same parameters for the H2 abstraction as in Andrews et al. (2016). Given the lack of data, we use the same parameters for the abstraction of H2, D2and HD. The cross section used comes from experiments on the deuteration of coronene, and cor- responds to a value of 0.06 Å2(Mennella et al. 2012). We consider the first abstraction as a barrierless process, and the second abstraction as involving a 0.01 eV barrier (Bauschlicher & Bakes 2001; Rauls & Hornekær 2008). The only difference between the rates comes from the mass of the atom colliding with the PAH.

Just like for the addition processes to PAHs in super states, we include a term of the form Pj =Nj,alip/(NH,alip + ND,alip), to consider the atom (in an aliphatic group) that the

colliding atom is more likely to abstract. When a j atom collides with an HD aliphatic group, we consider it is equally likely to abstract the H as to abstract the D. We assume this since we expect the energy difference to be insignificant.